Your webpack config only transpiles (and bundles) your frontend code. When you type npm start, node.js will execute server.js, which then includes your JSX source. Node does not support ES6 modules yet, so that's why it fails with a syntax error.

You can use the Babel require hook to automatically transpile the code for node. Don't forget to specify the 'es2015' and 'react' presets in the options.